Beatrice Acciaio: The Geometry of Adapted Optimal Transport

The Geometry of Adapted Optimal Transport

The adapted Wasserstein distance has been proven to be a suitable metric for comparing stochastic processes while accounting for their temporal structure, especially in a context of model uncertainty in finance. In this talk I will present our study of the geometry of the adapted Wasserstein space of stochastic processes.

We provide a probabilistic representation of absolutely continuous curves of processes, as well as an Eulerian representation via an adapted continuity equation, extending classical results of Wasserstein spaces to the adapted setting. Moreover, we characterize geodesics in this space, and from this derive an adapted Benamou-Brenier-type formula. I will then restrict the attention to Gaussian processes, where we can explicitly describe the solutions to the adapted Wasserstein transport, as well as the geodesics and the tangent space.

Based on joint works with D. Bartl, A. Grass, S. Hou, D. Krsek, G. Pammer, M. Rodrigues, S. Schrott.

BIO: Beatrice Acciaio is Professor of Mathematics at the Swiss Federal Institute of Technology -ETH Zurich since 2020. Before joining ETH, she was associate professor at the London School of Economics, and prior to that she has held positions at the University of Vienna and at the University of Perugia. Beatrice obtained her PhD in Applied Mathematics from the University of Perugia under the supervision of Walter Schachermayer. Her primary research interests are in stochastic analysis and optimal transports, and their applications in finance, insurance and economics, in particular concerning robust approaches to finance and decision-making under uncertainty. Beatrice is executive secretary of the Bachelier Finance Society, and Associate Editor for the SIAM Journal on Financial Mathematics, Finance and Stochastics, Mathematical Finance, Annals of Applied Probability, International Journal of Theoretical and Applied Finance, and the Bocconi & Springer Series on Mathematics, Statistics, Finance and Economics. Beatrice was awarded the 2022 Louis Bachelier prize for her contributions to financial mathematics.